Electroporation of cell membranes by electric pulses (EPs), also known as electropermeabilization, has been extensively studied for several decades. Experimental studies ranged from lipid bilayers and liposomes to both pro- and eukaryotic cells in culture and various tissues in vivo. Multiple theoretical studies explored the phenomenon of electropermeabilization by molecular dynamics, sophisticated electrical circuit modeling, and numerical simulations. Still, the mechanisms of electroporation itself and of electroporation-induced biological phenomena have not been fully understood, which stimulated a new surge of interest in the topic and numerous recent publications, e.g. [1-16].
In particular, electroporation has both well-established and developing applications for gene electrotransfer and gene therapy [15, 17-20] cell fusion [21-23], electro chemotherapy [24, 25], tumor ablation [4, 6, 14, 26], vascular smooth muscle cells ablation [5], sterilization [27, 28], and food processing [29, 30]. Numerous studies have focused on optimization of exposure conditions to produce maximum desired effect while minimizing side effects. However, with multiple parameters to consider (E-field, pulse duration, number of pulses, their shape, and repetition frequency) these studies have been laborious and showed limited success. The optimization process remains mostly empirical, whereas quantitative and mechanistic principles that determine the outcome of EP exposures are still being debated [8-11, 16, 31-33].
Out of different EP exposure parameters, the impact of the pulse repetition frequency (PRF) is the least understood, resulting in controversial findings and treatment recommendations. Aside from the trivial heating effect that increases with increased PRF (less time for heat dissipation), experimental and theoretical studies using different endpoints reported significantly greater bioeffects at higher PRF [2, 3, 14, 31, 34-37], significantly greater effects at lower PRF [1, 5, 6, 11, 26, 30, 38-40], biphasic or more complex dependences [31, 40, 41], or relatively little role of PRF within studied limits [2, 9, 40, 42].
Specifically, Vernier et al. [35] reported significant uptake of membrane impermeable dyes (propidium and YO-PRO-1) when Jurkat cells were exposed to 30 pulses (4-ns duration, 80 kV/cm) at 1 and 10 kHz rates. No dye influx was detected at the lower rates of 10 and 100 Hz. Jiang and Cooper [36] showed the reduction of the E-field threshold for nociceptor excitation from 30 to 24 and to 16 V/cm as the PRF was increased from 100 Hz to 1 and 4 kHz, respectively (for a train of one hundred 12-ns pulses). Similarly, applying 100-μs pulses at intervals under 1 ms lowered the electroporation threshold of artificial bilayer lipid membranes [34].
Increasing PRF from 0.1 to 1, 10, and 77 Hz (six 1-ms pulses at 800 V/cm) decreased the 24-hr survival of exposed CHO cells from 60% (0.1 Hz) to about 20% (77 Hz) [3]. Likewise, a train of 2,000 pulses (100-ns duration, 30 kV/cm) was more efficient in eliminating murine melanomas at PRF of 5 and 7 Hz when compared to 1 or 3 Hz [14]. However, the statistical significance of these findings was not evaluated. Overall, higher efficiency of higher PRF is usually attributed to the temporal summation of brief subthreshold effects (or lesions) which can recover without consequences if the interval between pulses is sufficiently long.
In contrast to the above studies, Rubinsky and co-authors observed more efficient cell killing at lower PRF, both in vitro and in vivo [5, 6, 26, 39]. The authors typically adjusted several exposure parameters at once (in order to keep the cumulative EP duration or the total dose unchanged), so isolating “pure” effects of PRF may be not straightforward. Still, one can find that, for example, eight 1-ms pulses at 2.5 kV/cm were more efficient at 0.03 Hz than at 0.3 Hz; or eighty 100-μs pulses at 2.5 kV/cm were more efficient at 0.3 Hz than at 3 Hz (see FIG. 2 in [26]). When the delivered energy was kept constant, longer exposures at the lower E-field and using a greater number of pulses typically was more efficient, despite lower temperature rise. Gradual enhancement of the cytotoxic effect as the PRF decreased from 5 kHz to 1 kHz, 60 Hz, and 1 Hz was also reported in SKOV3 cells exposed to exponentially-decaying EPs [38]. The reason for higher efficiency of lower PRF has not been identified, but it may be related to the reduction of EP efficiency when the cell membrane is made “leaky” by the previous EPs [10, 41]. With longer inter-pulse intervals, the membrane partially reseals and the efficiency of the coming pulses increases. Simulation studies showed an overall slow decrease of the fractional area of pores with PRF increase, however, with sharp regular troughs at certain frequencies [41].
Pucihar and co-authors [40] found that the uptake of Lucifer Yellow dye by DC3F cells exposed to 26 pulses of 30-μs duration was the same for 1 Hz and 8.3 kHz, however, it required about 1.5 times higher E-field for the higher PRF. The dependence was similar for 100-μs pulses, except for a slightly higher dye uptake at 10 Hz compared to both lower (1 Hz) and higher PRF (1 and 2.5 kHz).
For a train of 200 pulses of 50-μs at 0.9 kV/cm, the cytotoxic effect in CHO cells showed a bell-shaped dependence on PRF: it was weaker at the central frequency of 10 Hz, and gradually enhanced as the rate either decreased to 0.5 Hz or increased to 100 Hz [31]. At the same time, propidium uptake by the cells was flat for the range from 0.5 to 20 Hz, and increased at 50 and 100 Hz. The authors hypothesized that the increased cytotoxicity at the lowest PRF may be related to slow rotation of cells in suspension, so that different portions of their membrane get exposed to the field and more membrane is porated. This idea was later extended into a complex model that related random statistical rotations of suspension cells to EP efficiency [11].
In the field of electrochemotherapy, a significant effort has been made in recent years to compare 1 Hz and 5 kHz delivery rates of 100-μs pulses. The advantage of the 5 kHz PRF was alleviation of pain and discomfort from EP application, whereas its anti-tumor efficiency was either similar, or somewhat higher, or somewhat lower, depending on the concurrent conditions and the method of assessment (for discussion, see [1, 42-44]).